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ECON 34104410 LECTURE 7 Aggregate demand dynamics

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Title: ECON 34104410 LECTURE 7 Aggregate demand dynamics


1
ECON 3410/4410 LECTURE 7 Aggregate demand
dynamics
  • Ragnar Nymoen
  • 4 October 2007

2
Overview
  • Review of aggregate demand and its components.
  • Closed economy, open economy in a later lecture
  • Determinants of aggregate investments (ch 15) and
    consumption (ch 16), important and volatile
    components of aggregate demand
  • Aggregate demand put together,
  • and how monetary policy affects aggregate demand
    (ch 17)---the transmission mechanism.
  • Term structure of interest rates
  • Regime dependency of AD curve
  • Aggregate demand and aggregate supply
  • Short and long-run versions of the closed economy
    AS-AD model

3
Ch 15Private investment
4
Overview of Q-theory of investment
  • The market value of a firm is determined by
    discounting future dividends to the owners
  • By investing in capital, the firm grows and hence
    its capacity to generate dividends increases
  • The cost of investing one unit of capital is
    exogenous
  • This provides an incentive for firms with a high
    market value per unit of capital to invest
  • Definition q the ratio between the market
    value of the firm (V) and the replacement value
    of its capital stock (K)
  • Note Q-theory applied to housing investment
    (section 15.4) is cursory (you may drop it)

5
Pricing by arbitrage condition
  • Arbitrage condition In every period, stocks and
    bonds must yield the same risk-adjusted rate of
    return
  • Vt real stock market value of the firm at the
    start of period t
  • Vet1 expected real stock market value of the
    firm at the start
  • of period t1
  • De real expected dividend at the end of the
    period t
  • r real interest rate on bonds
  • ? risk premium on shares
  • In this way, markets for financial captial and
    real captial becomes integrated.

6
The fundamental value of a firm
  • Successive substitution of Vetj gives
  • Assume that the future value of the firm Vet1
    cannot rise faster than r ? (else it would be
    of infinite value), i.e.

7
The fundamental value of a firm
  • Then the infinite sum can be written as
  • What does this expression remind you of?
  • Interpretation The fundamental value of the firm
    equals the present value of expected future
    dividends
  • The role of the interest rate We only assume
    that the expected return on shares is
    systematically related to the return on bonds
  • What about investments? The firm must decide
    whether to pay out its profits now (as dividends)
    or invest it in order to increase profits
    (dividends) later Maximize Vt with respect to It

8
The decision to invest
  • Definition qt Vt / Kt the ratio between the
    market value of the firm and the replacement
    value of its capital stock
  • Expected value of the firm tomorrow
  • ? where we have used
    and
  • Cash flow constraint
  • ?e expected profit
  • c installation costs
  • Assume the following installation cost function

9
Optimal level of investment depends on q
  • Maximization of Vt taking qt as given gives the
    following first-order conditions

10
An example of the investment function
  • Assume that in order to simplify the
    value of the firm to
  • Assume furthermore that and
  • ? expected dividend pay-out ratio
  • ? constant profit share
  • Using the definition of q this gives the
    investment function

11
The general investment function
  • Abstracting from the functional form the general
    investment function is
  • E index of business confidence
  • Note that the risk premium is omitted
  • Note that in ch. 17 the level of capital K is
    assumed constant and the notation changes
    slightly (? is the index of business confidence)

12
Static investment function
  • Note that the rationale for assuming K constant
    (despite KtKt-1 It) is that K is a stock
    variable, while I is a flow variable.
  • Hence Kt is close to Kt-1 if the time period is
    short, even for large It
  • However, as we shall see, It may still react
    dynamically because of dynamics elsewhere in
    the full model.

13
Ch 16Private consumption
14
Overview of intertemporal consumption theory
  • Diminishing marginal utility of consumption
    provides an incentive for consumption smoothing
    over time.
  • Through the capital market, consumers can save or
    borrow and thus separate consumption from current
    income.
  • The discounted value of disposable lifetime
    income (human wealth) plus the initial stock of
    financial wealth represents the consumers
    lifetime budget constraint.
  • In optimum the consumer is indifferent between
    consuming an extra unit today and saving that
    extra unit in order to consume it tomorrow.
  • Current consumption will be proportional with
    wealth not income.
  • Note Issues on debt-financed tax cuts and
    Ricardian equivalence will be treated later on in
    the course.

15
Intertemporal consumer preferences
  • Representative consumer with a two-period utility
    function
  • Properties of the utility function
  • the marginal utility of consumption in each
    period is positive, but diminishing (provides an
    incentive for consumption smoothing)
  • the consumer is impatient the rate of time
    preference ? is positive

16
Intertemporal budget constraint
  • Period 1 budget constraint
  • Period 2 budget constraint
  • The consumers intertemporal budget constraint
  • V financial wealth
  • r real rate of interest
  • YL labour income
  • T net tax payment (taxes minus transfers)
  • C consumption

17
Human wealth and financial wealth
  • V1 represents the consumers initial financial
    wealth
  • The present value of disposable lifetime income
    can be thought of as human wealth (or human
    capital) H
  • This simplifies the notation of the intertemporal
    budget constraint

18
Optimal intertemporal consumption
  • Utility over the consumers life-time becomes (as
    a function of C1)
  • Maximization of U with respect to C1 gives the
    following first-order conditions
  • The Keynes-Ramsey rule

19
Optimal intertemporal consumption
  • In optimum, the marginal rate of substitution
    between present and future consumption (MRS) must
    equal the relative price of present consumption
    (1r)

20
Example of the consumption function with CES
utility
  • The constant (intertemporal) elasticity of
    substitution utility function
  • u(Ct) Ct-1/?
  • Insert this into the Keynes-Ramsey rule

21
Example of the consumption function with CES
utility
  • Insert the expression for the optimal C2 in terms
    of C1 into the intertemporal budget constraint.
  • Current consumption C1 is proportional to total
    current wealth (not current income).
  • The propensity to consume wealth is positive, but
    less than one.

22
The general consumption function
  • g growth rate of income (increases human
    wealth)
  • Some consumers may be credit constrained, hence
    Y1d
  • In chpt. 17 notation is slightly changed
  • The value of financial wealth is treated
    implicitly in r
  • ? is an index of consumer confidence (proxy for
    expected income growth)

23
Relationship to consumtion function in IDM
  • In IDM we had a consumption function with fewer
    explanatory variables, essentially only
    arguments, only Y-T.
  • We could have added r, for example, but left it
    out for simplicity.
  • On the other hand we introduced lagged C of
    course
  • The IDM specification thus assumes that
    adjustment of C to changes in Y-T for example is
    all done within the period of analysis.

24
Ch 17Aggregate demand
25
Overview over aggregate demand theory with
endogenous monetary policy
  • Private investments and consumption are sensitive
    to changes in the real interest rate, hence there
    is a potential for stabilization policy
  • The government cares about stabilizing both
    output and inflation
  • In order to achieve the governments objectives,
    the central bank sets the nominal short-term
    interest rate according to a Taylor rule
  • The resulting aggregate demand curve will be
    downwards-sloping in (y?) space
  • Important properties of the aggregate demand
    curve (the exact slope as well as the shift
    properties) will depend on the policy priorities
    (implied by the choice of coefficients in the
    Taylor rule)
  • Note We will return to questions about fiscal
    policy (public consumption and taxes) later in
    the course

26
Equilibrium condition in the goods market gives
the aggregate demand function Y
  • Investments plus consumption aggregate private
    demand D
  • Equlibrium condition for the goods market (closed
    economy)
  • Properties of the aggregate private demand
    function

27
Evidence from Denmark seem to confirm a close
relationship between private sector demand and
the real interest rate over time
The real interest rate and the private sector
savings surplus in Denmark, 1971-2000. Per cent
Source Erik Haller Pedersen, Udvikling i og
måling af realrenten, Danmarks Nationalbank,
Kvartalsoversigt, 3. kvartal, 2001, Figure 6
28
The long-run aggregate demand function in
log-linearized form
  • Assume that for that all arguments in the demand
    function are at their long-run (steady state)
    values, then long-run aggregate demand function
    is
  • The IAM textbook shows how the aggregate demand
    function Y can be log-linearized around its
    long-run equilibrium values to give

29
The real and the nominal interest rate
  • The definition of the expected real interest rate
  • As long as i and ? are close to zero, we can
    approximate the real interest rate
  • As a first approach we will assume static
    expectations

30
The Taylor-rule as a proxy for monetary policy
  • History shows that governments care about
    stabilizing both output and inflation.
  • As a proxy for these policy motives, we can use
    the following interest rate rule proposed by John
    Taylor
  • With this rule, y, ? and r will be on their
    long-run equilibrium values on average.
  • ? is interpreted as the inflation target (can be
    implicit or explicit).
  • For the stability of this economy, the parameter
    must be h positive so that an increase in
    inflation triggers an increase in the real
    interest rate (the Taylor principle).

31
Evidence from the euro area seems to confirm the
Taylor rule as a proxy for monetary policy
The 3 month nominal interest rate and an
estimated Taylor rate for the euro area,
1999-2003. Per cent
Source Centre for European Policy Studies,
Adjusting to Leaner Times, 5th Annual Report of
the CEPS Macroeconomic Policy Group, Brussels,
July 2003
32
Policy priorities implied by the Taylor rule
coefficients seem to vary across countries
Estimated interest rate reaction functions of
four central banks
1. Source Richard Clarida, Jordi Gali and Mark
Gertler, Monetary Policy Rules in Practice
Some International Evidence, European Economic
Review, 42, 1998, pp. 10331067. 2. Source
Centre for European Policy Studies, Adjusting to
Leaner Times, 5th Annual Report of the CEPS
Macroeconomic Policy Group, Brussels, July 2003.
33
Aggregate demand curve with endogenous monetary
policy
  • The log-linearized version of the aggregate
    demand function Y and the Taylor rule can be
    combined to an aggregate demand curve in (y?)
    space

34
The shape of the aggregate demand curve will
depend on the priorities of monetary policy
Illustration of the aggregate demand curve under
alternative monetary policy regimes (indicated by
the choice of coefficients h and b in the Taylor
rule)
35
The transmission mechanism Term structure of
interest rates
  • Remember that the rate of interest r in the
    demand function is interpretaable as an yield on
    long term bonds (10 years for example), a so
    called long interest rates
  • What monetary policy controls (directly or
    indirectly) is the very short interest rate, the
    money-market interest rate.
  • How can the central bank control the interest
    rate which is relevant for aggregate demand?
  • Answer No worry! When capital markets are
    operating according to theory a change in the
    money market rate will be transmitted
    automatically to the long rates!
  • Arbitrage is (again) the mechanism

36
The expectations theory of the term structure of
interest rates
  • Investment decisions depend on the expected cost
    of capital over the entire life of the asset
    (easily 10 years)
  • To what extend does the short-term policy rate
    influence long-term interest rates?
  • If short-term and long-term bonds are perfect
    substitutes (risk neutral investors) then the
    following arbitrage condition will hold
  • Taking logs and using the approximation ln(1i) ?
    I
  • Alternative Static interest rate expectations

37
In 2001, U.S. long-term interest rates kept a
steady level as the short-term policy rate fell
The Federal funds target rate (U.S. policy rate)
and the yield on 10 year U.S. government bonds,
2001-2002. Per cent
Source Danmarks Nationalbank
38
Whatever happened to the money market?
  • The Taylor-rule pushes the money market that we
    know from the IS-LM model into the background.
  • This is OK in many ways, as long as it does not
    lead to misunderstanding like
  • There is no role for money in the model
  • The money market is always, there it is only that
    it is not always specified explixtely.

39
The money market in a period-to-period equilibirum
Real Money supply
i
Real money demand L(Yt,it)
Mt/Pt
40
Consider a money targeting regime In each period
the money supply is set by the central bank.
Real Money supply in period t
i
Interest rate in peride t
Real money demand L(Yt,it)
Mt/Pt
41
Interest rate function in a money targeting regime
The money graph in previous slide defines
it i(Yt, Mt/Pt) where Y and
M/P are regarded as determined outside the money
market, M/P being the policy instrument.
  • If we define a long-run interest rate by
    inserting the long run values of the arguments in
    the i-function and then take the deviation
    between it and the long-run rate, we obtain a
    function that is qualitatively similar to the
    Taylor-rule. With one important difference
  • In the money targeting regime the derivatives of
    the i-function are already given by the
    properties of the money demand function.
  • In the Taylor-rule the corresponding parameters h
    and b transpires to be free parameters, to the
    chosen by the central bank (see next lecture)
  • Note IAM p 504-506 contains a more detailed
    comparison/derivation of the two interest rate
    functions

42
The money market with a policy determined
interest rate
If the coefficients of the Taylor-rule are
free-parameters, the money market operates like
this
i
Interest rate in period t
M/P
Real money supply In period t
Real money supply is then an endogenous variable.
Since the price level is pre-determined in any
given period, it is the nominal money stock that
adjusts immediately to bring the market into
equilibrium. The Central Bank does this by
market operations.
43
The AD-schedule is regime dependent
  • Although it is OK for some purposes to use the
    Taylor-rule as a catch all for monetary policy,
    as IAM does, it is also obscuring the important
    fact that
  • The response of aggregate demand (the impact
    multipliers of you like) to for example an
    increase in g is dependent on the monetary policy
    regime.
  • This point is going to be even more important
    when we later move to the open economy.

44
Aggregate demand dynamics---where is it?
  • This lecture was titled aggregate demand dynamics
  • But the main impression is that we have
    simplified so much that dynamics have almost been
    removed from the demand side.
  • Still there is one source of dynamics left the
    real interest rate is and expectations
    variable---which is a source of dynamics.
  • In the next lecture we will utilize this to
    establish a long-run and a short-run version of
    the AD-AS model.
  • We will also consider a different model
    altogether the real-business cycle model, where
    dynamics stems form other sources than
    expectations.
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